Pythagoras and irrational
numbers: For any right-angled triangle where c is the hypotenuse and a and b are the other two sides then a^{2} + b^{2} = c^{2.} |
Pythagoras was so pleased when he discovered this relationship that he sacrificed an ox. Sadly, the Pythagoreans also believed that any real length could be expressed as the ratio of 2 integers. When it was shown by Hippasus that a triangle with unit sides had a hypotenuse which defied any such expression (i.e. an irrational number, the square root of 2) Hippasus was drowned for his heresy and the Pythagorean school sworn to secrecy. Or so legend has it. |